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Rainbow Trees in Hypercubes

Published: August 19, 2025 | arXiv ID: 2508.14186v1

By: Nicholas Crawford , Maya Sankar , Carl Schildkraut and more

BigTech Affiliations: Stanford University

Potential Business Impact:

Finds hidden paths in computer networks.

Business Areas:
A/B Testing Data and Analytics

We prove that every proper edge-coloring of the $n$-dimensional hypercube $Q_n$ contains a rainbow copy of every tree $T$ on at most $n$ edges. This result is best possible, as $Q_n$ can be properly edge-colored using only $n$ colors while avoiding rainbow cycles.

Country of Origin
🇺🇸 United States

Page Count
18 pages

Category
Mathematics:
Combinatorics